Enabling hostapd and udhcpd to start at each Pi's boot:
Since the IP address mentioned in interfaces files wasn't assigned to wlan0 in every boot (bizarre), I had to come up with the following workaround. This, because without an IP assigned to wlan0, the DHCP deamon wouldn't start, thus the Pi wouldn't distribute an IP to any client willing to pair with your Pi.

Enabling hostapd and udhcpd to start at each Pi's boot:
Since the IP address mentioned in interfaces files wasn't assigned to wlan0 in every boot (bizarre), I had to come up with the following workaround. This, because without an IP assigned to wlan0, the DHCP deamon wouldn't start, thus the Pi wouldn't distribute an IP to any client willing to pair with your Pi.

UPDATE - 2019-02-10: Yeah, I finally managed to create a working access point with the TL-WN725N.

It looks like the standard driver r8188eu for RTL8188EUS chipset from the package "firmware-realtek" is not working with hostapd on Raspbian Stretch. After lots of trial and error and using deprecated tutorials I found out, that hostapd is working with the driver from MrEngman. There is no patched hostapd necessary, simply update the driver for the wifi dongle. Here is what I did: